Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeTangents & NormalsEasy2 minPYQ_2009

MathematicsEasysingle choice

The value of $a$ in order that $f (x) = sin x - cos x - a x + b$ decreases for all real values is given by

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Answer:

Solution:

We have; $f (x) = sin x - cos x - a x + b$ $\Rightarrow f^{'} (x) = cos x + sin x - a$ $\Rightarrow f^{'} (x) < 0 \forall x \in R$ $\Rightarrow (cos x + sin x) < a \forall x \in R$ As the max. value of $(cos x + sin x)$ is $2$ The above is possible when $a \geq 2$

Stream:BITSATSubject:MathematicsTopic:Application of DerivativeSubtopic:Tangents & Normals

⏱ 2mℹ️ Source: PYQ_2009

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